Artificial Immune System Dynamics Model And Its Application In Optimization And Control

The stability of positive equilibrium and bifurcation of the reaction model of immune system and dynamic model of immune network, as well as the dynamic behavior of Marchuk immune system under different parameters are studied in the dissertation. The theories and methods of the network model of immune system in optimization and application are discussed.Firstly, based on the previous studies for the reaction model of Marchuk immune system, the stability of positive equilibrium solution of Marchuk model and the condition for producing Hopf bifurcation and periodic solution are studied using system dynamics, in addition, the dynamic behavior under different parameters are simulated on computer. Next, the dynamic model of Perelson immune system is extended for the case with a time lag, moreover, the sufficient condition that the immune system either without time lag or with arbitrary time lag has positive equilibrium solution is drawn. Then, integral transformation is utilized to transform AB network model into replicator dynamical equations, and the Nash equilibriums of AB network model is studied by using evolutionary game approach. As to the farmer network model, its stability and attractability of equilibriums are studied using Lyapunov function and the sufficiency condition is deduced.Secondly, as to the shortcomings existent in immune algorithm, chaotic searching mechanism is introduced, in which a Henon mapping is employed to replace other chaotic mappings to generate a uniform distribution chaotic sequence, thus improving searching performance and convergence speed. On the other hand, traditional multi-objective optimization approaches are computationally expensive, resulting low convergence speed and often failing in finding the Pareto optimal about given problems. Thus, a new ranking scheme for multi-objective optimization is proposed to improve traditional approaches, which can generate much more Pareto optimal with uniform distribution in a larger domain.Finally, on the basis of previous researches in immune network dynamics model, it is applied in immune algorithm design in this paper. Then, an artificial immune network is first proposed using the replicator dynamical equations in evolutionary game theory, which exactly describes the evolutionary game relationship between antibodies and is applied in pattern learning. The immune network dynamics is used...